# Derivative wrt one variable of an integral wrt another

1. Mar 11, 2012

### apb000

I can't seem to find this anywhere. What's
d/dn(∫ n(w) dw)?

That's the derivative wrt n of the integral of n over w (note: n is a function of w). Seems straightforward enough. Is there a simplification?

Thanks

2. Mar 11, 2012

### mathman

The notation you are using to express what you want is confusing. Under the integral sign, n is a function. Outside it is a variable.

3. Mar 11, 2012

### HallsofIvy

Staff Emeritus
But a function is a variable! One can always define the derivative of y with respect to a function, f(x)- dy/dx= (dy/df)(df/dx) so dy/df= (dy/dx)/(df/dx).

So $d/df \int f(x)dx= (d(\int f(x)dx)/dx)(df/dx)= f(x)(dy/dx)$.

4. Mar 12, 2012

### mathman

Where did y come from?